Array
(
    [fullTitle] => Questioning Gödel's Ontological Proof: Is Truth Positive?
    [abstract] => In his “Ontological proof”, Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false. 
    [authors] => Array
        (
            [0] => Array
                (
                    [givenName] => Gregor
                    [affiliation] => Martin Luther University of Halle-Wittenberg
                )

        )

    [keywords] => Array
        (
        )

    [doi] => 10.24204/ejpr.v3i1.386
    [datePublished] => 2011-03-21
    [pdf] => https://www.philosophy-of-religion.eu/menuscript/index.php/ejpr/article/view/386/version/330/357
)
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Questioning Gödel's Ontological Proof: Is Truth Positive?

Gregor
Martin Luther University of Halle-Wittenberg

DOI: https://doi.org/10.24204/ejpr.v3i1.386

Abstract

In his “Ontological proof”, Kurt Gödel introduces the notion of a second-order value property, the positive property P. The second axiom of the proof states that for any property φ: If φ is positive, its negation is not positive, and vice versa. I put forward that this concept of positiveness leads into a paradox when we apply it to the following self-reflexive sentences: (A) The truth value of A is not positive; (B) The truth value of B is positive. Given axiom 2, sentences A and B paradoxically cannot be both true or both false, and it is also impossible that one of the sentences is true whereas the other is false. 

Keywords:

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